Define "almost". Nothing is rigid enough to remain static across an event horizon.

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.---If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

Eebster the Great wrote:Not sure I understand the question. The reference frame is a specific event at a specific velocity. That's where and when you make the measurement. You measure the geodesic distance. It has to be symmetrical . . .

In special relativity, simply specifying an object's velocity as its worldline passes through a given event is enough to define a unique inertial rest frame. But in general relativity this would only be enough to specify a unique "local" inertial rest frame in the infinitesimal spacetime neighborhood of the event; if you want a coordinate system that covers a large region of curved spacetime, it will automatically be a non-inertial coordinate system, and you can find an infinite number of different non-inertial coordinate systems where a given object is at rest at a given point. So you have to specify the full coordinate system (or at least the full definition of simultaneity) in order to have a unique "smallest distance" between two events which are simultaneous in that coordinate system.

As close to Born-rigid as possible without creating Ehtenfest's paradox when it rotates.

Yakk wrote:Maybe he means relatively far away from a relatively light body, like, I dunno, a few meters away from the surface of the sun?

That is what I meant.

If you're talking about a region where the tidal forces across the meter-stick would be negligible (like near the surface of the Sun), then if the meter is in freefall (falling or in orbit) the equivalence principle would imply the forces between magnets on each end should be nearly identical to the forces that would be observed if the same meter stick with magnets was moving inertially in flat spacetime. If the ends are undergoing something close to Born rigid acceleration, then presumably the forces between the magnets would be the same as for a meter-stick-with-magnets undergoing Born rigid acceleration in flat spacetime.

I take an instrument that measures all the properties of a magnetic field at a given point. I measure the magnetic field around the magnets at several points in both locations. The large body does not produce a magnetic field. Will my results change between the two locations?

jewish_scientist wrote:Why does the speed of light through a vacuum have to be constant?

That's a great question. The fact is, it's not something that "has" to be true, it's just one of the assumptions that leads to special and then general relativity (the other being that observers in non-accelerating reference frames will agree on a bunch of properties). Then large amounts of experimental evidence shows that SR and GR predict various phenomena much better than Galilean/Newtonian physics on the cosmological scale.

That said, it's not really "the speed of light is constant" that is the real trick. The trick is that if you take Maxwell's Equations of electrodynamics as accurate, then they predict a direct relationship between the speed at which an electromagnetic field propagates and two properties about how a vacuum deals with electromagnetic fields passing through it, and since those shouldn't depend on your frame of reference because of how they're defined, neither should the speed of electromagnetic field propagation. Then you get the revelation that light is just an electromagnetic field propagation and the rest follows.

(As a small note, "constant" isn't really the right word, because that means "not changing over time" and time isn't really the thing we're worried about. The more accurate term is "invariant", which roughly means "regardless of your frame of reference". There have been some papers proposing a changing value of c as the universe ages, and while they have their own problems they don't, in themselves, inviolate SR or GR.)

ConMan wrote:(As a small note, "constant" isn't really the right word, because that means "not changing over time" and time isn't really the thing we're worried about. The more accurate term is "invariant", which roughly means "regardless of your frame of reference". There have been some papers proposing a changing value of c as the universe ages, and while they have their own problems they don't, in themselves, inviolate SR or GR.)

Today I learned "physical constant" has specific semantics. Or at least ConMan and wikipedia agree that a physical constant is only and exactly constant over time. (I thought constant was constant with respect to a system —in case of our universe, constant in spacetime)

I think the meanings are pretty much the same. Something that is constant doesn't change from one day to the next. I don't think that most people who consider the word "constant" think about Lorentz boosts.

Electromagnetism is best described my Maxwell's Equations. Maxwell's Equations predict that electromagnetic waves should travel at a constant speed in a vacuum regardless of the observer. The electromagnetic force is associated with photons. Photons are the fundamental component of light. Taken all together, electromagnetism is best described when the speed of light through a vacuum is constant regardless of the observer.

I am assuming that Maxwell did not realize this because Einstein had not invented/discovered Special Relativity yet. In fact, Einstein invented/discovered Special Relativity to explain why Maxwell's Equations do not violate relativity.

Pretty much. It's worth noting that people were well aware of this problem before Einstein though (even if it did take them a long time to properly identify the symmetries of Maxwell's equations) and that this is the main issue the luminferous æther was supposed to solve; it could act as a preferred reference frame in which EM took place and its nice Maxwell form whilst physics as a whole still used galilean relativity.

Maxwell's Equations are a synthesis of relationships (Gauss, Ampere, and Faraday) that had been determined from observations (many). Faraday originated the idea of a field, but he didn't have the math background to give it a formal treatment.

A minor quibble. Everything in science "comes from observations", although you did clarify what you meant by that.

thoughtfully wrote:As usual QM seems to be crashing the party. But at least it fixes those awful singularities and other problems.

That Scharnhorst effect is interesting, but it only appears problematic if you define c to be the speed of light in a normal vacuum. If you use the more fundamental definition that it's the constant relating space to time in the formula for the spacetime interval in flat space:

s2 = x2 - c2t2

then everything's fine, and we can say that light normally travels at slightly slower than c in a normal vacuum, and a little faster (but still less than c) in a Casimir vacuum. Equivalently, c is the theoretical speed of a fictitious naked photon in a fictitious naked vacuum, i.e., neither the photon nor the vacuum have associated virtual particles.

PM 2Ring wrote:That Scharnhorst effect is interesting, but it only appears problematic if you define c to be the speed of light in a normal vacuum. If you use the more fundamental definition that it's the constant relating space to time in the formula for the spacetime interval in flat space:

s2 = x2 - c2t2

then everything's fine, and we can say that light normally travels at slightly slower than c in a normal vacuum, and a little faster (but still less than c) in a Casimir vacuum. Equivalently, c is the theoretical speed of a fictitious naked photon in a fictitious naked vacuum, i.e., neither the photon nor the vacuum have associated virtual particles.

This is interesting. So if we measure the speed of light in intergalactic space, we would expect that to be slightly less than the "c" from special relativity?

Not in the form of radiation. A magnetic field of a massy object doesn't spend any of its time interacting as a particle.

Edit: I did say "field" and not "wave". I can't figure out what you're talking about. Light has an EM field....

Edit again: Let me rephrase this in the form of a question. The gravitational or magnetic influence of a massy or magnetic object propagates at c, because that is the upper limit at which information can propagate in the universe. If the real-life speed of light as in the wavicle moving in a vacuum is hampered by quantum effects, that would be independent of c, yes? A quirk of photons that has nothing to do with c, and just makes the use of "speed of light" to mean c even less relevant than it already was, since it's actually a very, very, very slightly different number?

So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

Xanthir wrote:Light is literally an EM wave. Magnetism is transmitted by photons. If photons are very slightly slowed down from c by virtual particles, then "magnetic force" is too, because it's literally photons.

The magnetic field is not "literally photons" which is his whole point.

How is the magnetic field not photons? What does photon mean to you? For me, a photon is a little shortcut for talking about the particle-ish behavior in QED, but not so important. Light and magnetism are both just shades of QED. If you want to split out the radiative term in a propogating field as the 1/r^2 bit (I think it was that term that gets that name) and give it a special "radiation" name, then you can do that, but all these things are photons.

Also Copper Bezel is a woman.

LE4dGOLEM: What's a Doug?Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Yeah it is so totally not like how a water wave is made up of particle like molecules, but then exhibit some special wave behavior in bulk.Fields all the time, wave and particle are just weird classical analogies that work more or less well depending on which you way squint.

LE4dGOLEM: What's a Doug?Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Yeah, precisely that. A single photon acts wave-like if you poke it the right way. An EM wave acts like a single "particle" of energy if you poke it the right way. Both are just interpretations of EM field excitations that can be useful for thinking about energy in different situations, but both are incomplete/incorrect in general.

And because of this, if "photons" are slowed down by the virtual-particle stew to slightly less than c, then magnetic field propagation is slowed down exactly the same, because they're literally the same thing experiencing the same phenomenon.

It's not wavicles I don't understand, it's fields. So the static, uninteresting, can-do-no-work EM fields that hold my molecules together and hold magnets to fridges are themselves mediated by photons?

So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

Yup. Though it's only the static M part that does no work, and not all fields are static anyway. "Field" is a much broader concept, but even the narrow static boring bits can be quantized and when this happens, you can observe photons.

LE4dGOLEM: What's a Doug?Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Gotcha. I mean, I don't get it get it, but it does answer my original question, and now I can go look up something on quantization in magnetic fields etc. to see if I can follow that better than previously.

So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

It's probably worth pointing out that in quantum field theories, the fields aren't actual physical fields like the electric field or magnetic fields but an underlying abstraction from which observables are derived. The matter particles such as electrons and muons are fields as well as the photons pertubations that get tossed about among them.

I think that could have been written with more clarity, sorry. Somebody already has. Feynman's QED: A theory of light and matter is quite accessible, affordable, and still a classic.

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.-- Antoine de Saint-Exupery

doogly wrote:How is the magnetic field not photons? What does photon mean to you? For me, a photon is a little shortcut for talking about the particle-ish behavior in QED, but not so important. Light and magnetism are both just shades of QED. If you want to split out the radiative term in a propogating field as the 1/r^2 bit (I think it was that term that gets that name) and give it a special "radiation" name, then you can do that, but all these things are photons.

The radiative term is exactly what I was talking about, and from Copper Bezel's post it sounds like exactly what she was talking about, given her post started "not in the form of radiation". If you want to call the EM field a photon field, that's fine, but saying it is "made of photons" doesn't make a whole lot of sense. It sounds to me equivalent to saying the Higgs field is "made of Higgs bosons" (though I guess with enough acceleration...).

Can I derail for a second to ask?: thoughtfully mentioned Feynman's QED - how accessible is the text/what level of knowledge does it assume, and how much ground does it cover? I have a very superficial grasp of QFT which I would like to expand on, is all.